The course aims to show practical methods of solving problems encountered in science and engineering. The numerical solution of systems of differential equations is discussed, and parallel cooperation of microprocessors based on differential calculus is evaluated.  The course mainly examines VSVO (variable step, variable order) methods. During the course, students are going to use an original method based on a direct calculation of the Taylor series terms. The TKSL (FOS) simulation language is also available, which allows specifying problems directly using equations.
The close correspondence of block and equation representations of differential equations is also analysed, using block representation as input. The course discusses the following technical problems: solution of large systems of differential equations, algebraic equations, partial differential equations, stiff systems, problems in automatic control, electric circuits, VLSI circuits, modelling of mechanical systems, electrostatic and electromagnetic fields. The analysis of the parallel algorithms and design of a specialised architecture for the solution of differential equations is also part of the course. Most of the technical problems lead to the matrix/vector representation. Individual problems are also going to be solved in MATLAB/Simulink.

Areas of interest for SDZ

1. Analytical solution of differential equations.
2. Numerical solution of differential equations.
3. Extremely accurate solution of differential equations using the Taylor series, libraries for accurate calculations.
4. Parallel properties of the Taylor series, the basis of the programming of the specialised parallel tasks using differential calculus (close correspondence of block and equation representation).
5. The adjunct differential operators and parallel solution of the differential equations with time-variable coefficients.
6. The solution of large systems of algebraic equations by converting them to the ordinary differential equations..
7. Fourier series, finite integrals.
8. Simulation of electric circuits.
9. Solution of practical problems described by partial differential equations.
10. The concept of a basic specialized processor for parallel computational system.